Oenothera analyses, updated Dec 28 2020
Questions we are exploring
Do floral traits vary across populations?
If floral traits vary across populations, are patterns of variation clinal, associated with variation in pollinators, or random?
In this file:
I provide a list of potential variables/approaches to consider to address the questions above. I then provide the results of most of these analyses, with the caveat that results may shift slightly after we account for response factors in the scent emission data and potentially clean up some erroneous values in the morphology data.
Floral traits that could vary
Overall approach: I think we are investigating whether differences between populations occur in floral morphology, floral scent, or a combination of the two.
(To facilitate our analyses, we reduced the number of floral scent variables under investigation by combining correlated compounds that are produced via the same biosynthetic pathways. I will make a supplement/appendix for the paper that shows how we did that.)
So, we can start with multivariate approaches that use the morphology variables, the scent variables, or both, and see how much of the total variance those approaches explain.
Then, we can unpack which variables in particular are different across populations.
Total emission rate and compound diversity are two variables that are essentially summaries of the whole scent dataset, so they won’t be included in the multivariate analyses, but will be analyzed regardless of the outcomes of the multivariate analyses.
| Trait | Approach |
|---|---|
| Floral scent, total emission rate | Linear mixed model analysis across populations of total emission rates in toluene equivalents |
| Floral scent, compound diversity | Linear mixed model analysis of the number of compounds in samples across populations |
| Floral scent, blend composition | Multivariate analysis (e.g. Adonis) plus constrained ordination. Currently using emission rates in toluene equivalents, will ultimately convert this to emission rates adjusted for response factors. |
| We are doing this using emission rates that are the sums of all compounds produced from a certain biosynthetic cluster/table. | |
| Floral scent, emission rates of key compounds or compound groups | 1. identify what the key compound(s)/compound group(s) are from the constrained ordination. |
| 2. linear mixed model analysis to compare across populations. | |
| Floral morphology | Multivariate analysis (e.g. Adonis) plus constrained ordination, followed by univariate mixed model analyses of key variables. |
| Scent & morphology together | Multivariate analysis (e.g. Adonis) plus constrained ordination |
Total emission rate
This is total emission rate (per g fresh mass) as a function of population, with plant nested within population as a random effect. So this makes use of all measured flowers.
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Comp.Total ~ Population + (1 | Pop_Plant)
## Data: ER_f_mass
##
## REML criterion at convergence: 3212.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.136 -0.371 -0.090 0.212 3.212
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 41488296 6441
## Residual 44481777 6669
## Number of obs: 157, groups: Pop_Plant, 72
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 5936.19 1790.52 62.93 3.315 0.001522 **
## PopulationZion 5465.22 3387.55 75.10 1.613 0.110869
## PopulationInyo 10785.17 2829.70 69.39 3.811 0.000296 ***
## PopulationArizona 8772.25 2353.84 59.75 3.727 0.000433 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnZ PpltnI
## PopulatinZn -0.529
## PopulatnIny -0.633 0.334
## PopultnArzn -0.761 0.402 0.481ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 857042809 285680936 3 68.624 6.4224 0.0006734 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Logan 5936 1795 64.2 2351 9522
## Zion 11401 2878 81.8 5675 17128
## Inyo 16721 2195 75.5 12350 21093
## Arizona 14708 1531 56.9 11642 17775
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Logan - Zion -5465 3392 76.5 -1.611 0.3785
## Logan - Inyo -10785 2835 70.7 -3.804 0.0017
## Logan - Arizona -8772 2359 61.0 -3.718 0.0024
## Zion - Inyo -5320 3620 79.4 -1.470 0.4604
## Zion - Arizona -3307 3260 75.5 -1.014 0.7416
## Inyo - Arizona 2013 2676 68.8 0.752 0.8754
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 4 estimates
Interpretation: total scent shows a roughly clinal pattern. Due to the amount of variance, the significant contrasts are that Logan has lower total scent than Inyo or Arizona. Zion is intermediate.
Compound diversity
This is the number of compounds detected in a sample as a function of population, with plant nested within population as a random effect. So this makes use of all measured flowers.
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Total ~ Population + (1 | Pop_Plant)
## Data: P_A_totals
##
## REML criterion at convergence: 854.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.59687 -0.51638 0.09328 0.60457 1.60926
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 10.342 3.216
## Residual 9.245 3.040
## Number of obs: 155, groups: Pop_Plant, 72
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 12.9716 0.8775 64.7604 14.782 < 2e-16 ***
## PopulationZion 2.7123 1.6382 73.2571 1.656 0.10206
## PopulationInyo 4.6145 1.3733 68.7880 3.360 0.00127 **
## PopulationArizona 3.2289 1.1495 60.7459 2.809 0.00668 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnZ PpltnI
## PopulatinZn -0.536
## PopulatnIny -0.639 0.342
## PopultnArzn -0.763 0.409 0.488ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 121.18 40.395 3 67.738 4.3695 0.007147 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Logan 13.0 0.880 66.8 11.2 14.7
## Zion 15.7 1.384 79.0 12.9 18.4
## Inyo 17.6 1.058 73.8 15.5 19.7
## Arizona 16.2 0.744 57.5 14.7 17.7
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Logan - Zion -2.712 1.64 75.3 -1.654 0.3554
## Logan - Inyo -4.614 1.38 70.8 -3.354 0.0069
## Logan - Arizona -3.229 1.15 62.7 -2.803 0.0332
## Zion - Inyo -1.902 1.74 77.1 -1.092 0.6956
## Zion - Arizona -0.517 1.57 73.6 -0.329 0.9876
## Inyo - Arizona 1.386 1.29 67.9 1.072 0.7079
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 4 estimates
Interpretation: The total number of compounds also shows a clinal pattern. The significant contrasts are that Logan has fewer compounds than Inyo and Arizona.
Floral scent blend composition, multivariate analyses using groupings by biosynthetic pathway
Note: these results could change once we are working with emission rates adjusted for response factors
These are the groupings of the compounds (ver. 2.0):
| Code | Compounds |
|---|---|
| G.ILE | 2 methylbuyronitrile, nitro-2-methyl butane, cis-2-methylbutyraldoxime, trans-2-methylbutyraldoxime |
| G.LEU | 3methylbutyronitrile, nitro-3-methyl-butane, cis-3-methylbutyraldoxime, trans-3-methylbutyraldoxime, cis-isobutyraldoxime, trans-isobutyraldoxime |
| G.PHE | 2phenylethanol, phenylacetonitrile, nitrophenylethane, phenylacetaldoxime |
| G.OCI | b-myrcene, cis-b-ocimene, trans-b-ocimene |
| G.GER | citronellol, neral, geranial, nerol, geraniol |
| G.LIN | linalool |
| G.LOX | cis-furanoid-linalool-oxide, trans-furanoid-linalool-oxide, pyran-lin-oxide-ketone, cis-pyranoid-linalool-oxide, trans-pyranoid-linalool-oxide |
| G.CAR | beta-caryophyllene, alpha-humulene, caryophyllene-oxide, farnesol |
| G.NER | nerolidol |
| G.ISO | isophytol |
| G.ALT | alpha-terpineol |
| G.FAR | beta-farnesene, Z-E-alpha-farnesene, E-E-alpha-farnesene, farnesene-epoxide |
First, running an adonis (comparable to ANOSIM):
##
## Call:
## adonis(formula = ER_f_mass_group_data ~ Population, data = ER_f_mass_groups, permutations = 999, method = "bray")
##
## Permutation: free
## Number of permutations: 999
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## Population 3 3.4156 1.13853 6.2947 0.22512 0.001 ***
## Residuals 65 11.7567 0.18087 0.77488
## Total 68 15.1723 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Interpretation: The adonis shows a significant effect of population, which explains about 23 % of the variance in scent blend composition.
Running a constrained analysis of principle coordinates:
##
## Call:
## capscale(formula = ER_f_mass_group_data ~ Population, data = ER_f_mass_groups, distance = "bray")
##
## Partitioning of squared Bray distance:
## Inertia Proportion
## Total 16.979 1.0000
## Constrained 3.499 0.2061
## Unconstrained 13.481 0.7939
##
## Eigenvalues, and their contribution to the squared Bray distance
##
## Importance of components:
## CAP1 CAP2 CAP3 MDS1 MDS2 MDS3 MDS4
## Eigenvalue 3.2414 0.130950 0.126292 3.1226 2.3205 1.7721 1.25862
## Proportion Explained 0.1909 0.007712 0.007438 0.1839 0.1367 0.1044 0.07413
## Cumulative Proportion 0.1909 0.198617 0.206055 0.3900 0.5266 0.6310 0.70512
## MDS5 MDS6 MDS7 MDS8 MDS9 MDS10 MDS11
## Eigenvalue 0.95712 0.7692 0.5960 0.52174 0.36536 0.28894 0.25091
## Proportion Explained 0.05637 0.0453 0.0351 0.03073 0.02152 0.01702 0.01478
## Cumulative Proportion 0.76149 0.8068 0.8419 0.87263 0.89414 0.91116 0.92594
## MDS12 MDS13 MDS14 MDS15 MDS16 MDS17
## Eigenvalue 0.20075 0.18159 0.17264 0.129959 0.103850 0.088593
## Proportion Explained 0.01182 0.01069 0.01017 0.007654 0.006116 0.005218
## Cumulative Proportion 0.93776 0.94846 0.95863 0.966279 0.972396 0.977613
## MDS18 MDS19 MDS20 MDS21 MDS22 MDS23
## Eigenvalue 0.07979 0.06487 0.044465 0.043061 0.037929 0.02649
## Proportion Explained 0.00470 0.00382 0.002619 0.002536 0.002234 0.00156
## Cumulative Proportion 0.98231 0.98613 0.988752 0.991288 0.993522 0.99508
## MDS24 MDS25 MDS26 MDS27 MDS28
## Eigenvalue 0.023999 0.0169519 0.0165729 0.0115865 0.0058020
## Proportion Explained 0.001413 0.0009984 0.0009761 0.0006824 0.0003417
## Cumulative Proportion 0.996496 0.9974939 0.9984700 0.9991524 0.9994941
## MDS29 MDS30 MDS31 MDS32
## Eigenvalue 0.0031433 0.002802 0.002479 1.647e-04
## Proportion Explained 0.0001851 0.000165 0.000146 9.697e-06
## Cumulative Proportion 0.9996792 0.999844 0.999990 1.000e+00
##
## Accumulated constrained eigenvalues
## Importance of components:
## CAP1 CAP2 CAP3
## Eigenvalue 3.2414 0.13095 0.1263
## Proportion Explained 0.9265 0.03743 0.0361
## Cumulative Proportion 0.9265 0.96390 1.0000
##
## Scaling 2 for species and site scores
## * Species are scaled proportional to eigenvalues
## * Sites are unscaled: weighted dispersion equal on all dimensions
## * General scaling constant of scores:The constrained portion explains about 21% of overall distance. CAP1 explains about 19% and CAP2 expalins about 1% of overall distance. I suggest this means we should really be looking at the compounds that are correlated with CAP1
Plotting the capscale:
Checking to see which compound group(s) are significantly correlated with CAP1 and/or CAP2.
| compounds | cor1 | p1 | cor2 | p2 | sig1 | sig2 |
|---|---|---|---|---|---|---|
| G.ILE | 0.4839 | 0.0001 | -0.2587 | 0.0792 | Yes | No |
| G.LEU | 0.5139 | 0.0000 | 0.2571 | 0.0792 | Yes | No |
| G.PHE | -0.1889 | 0.2057 | 0.1049 | 0.4699 | No | No |
| G.OCI | -0.0091 | 0.9409 | 0.54 | 0.0000 | No | Yes |
| G.GER | 0.1506 | 0.2603 | -0.1048 | 0.4699 | No | No |
| G.LIN | 0.6951 | 0.0000 | 0.0645 | 0.6527 | Yes | No |
| G.LOX | -0.1395 | 0.2761 | -0.2897 | 0.0630 | No | No |
| G.CAR | -0.2239 | 0.1287 | -0.1054 | 0.4699 | No | No |
| G.FAR | -0.1681 | 0.2232 | 0.4281 | 0.0015 | No | Yes |
| G.NER | -0.1684 | 0.2232 | -0.0425 | 0.7291 | No | No |
| G.ISO | 0.2682 | 0.0621 | 0.1536 | 0.3562 | No | No |
| G.ALT | 0.3538 | 0.0086 | 0.1726 | 0.3124 | Yes | No |
This table indicates that six compound groups are correlated with CAP1 at P adjusted < 0.01 : ILE, LEU, LIN, ALT. Two compound groups are correlated with CAP2: OCI, FAR.
Floral scent, univariate analyses of key compound groups
Note: these results could change once we are working with emission rates adjusted for response factors. Also will need to check for p-value adjustments for performing mulitple tests (e.g. one test for each compound group).
For each compound group that was correlated with CAP1 and/or CAP2, the emission rate is modeled as a function of population, with plant nested within population as a random effect. This uses data from all measured flowers.
ER_f_mass_groups <- ER_f_mass %>% mutate(G.ILE=Comp.2methylbutyronitrile+`Comp.nitro-2-methyl-butane`+`Comp.cis-2-methylbutyraldoxime`+`Comp.trans-2-methylbutyraldoxime`,
G.LEU=Comp.3methylbutyronitrile+`Comp.nitro-3-methyl-butane`+`Comp.cis-3-methylbutyraldoxime`+`Comp.trans-3-methylbutyraldoxime`+`Comp.cis-isobutyraldoxime`+`Comp.trans-isobutyraldoxime`,
G.PHE=Comp.2phenylethanol+Comp.phenylacetonitrile+Comp.nitrophenylethane+Comp.phenylacetaldoxime,
G.OCI=`Comp.b-myrcene`+`Comp.cis-b-ocimene`+`Comp.trans-b-ocimene`,
G.GER=Comp.citronellol+Comp.neral+Comp.geranial+Comp.nerol+Comp.geraniol,
G.LIN=Comp.linalool,
G.LOX=`Comp.cis-furanoid-linalool-oxide`+`Comp.trans-furanoid-linalool-oxide`+`Comp.pyran-lin-oxide-ketone`+`Comp.cis-pyranoid-linalool-oxide`+`Comp.trans-pyranoid-linalool-oxide`,
G.CAR=`Comp.beta-caryophyllene`+`Comp.alpha-humulene`+`Comp.caryophyllene-oxide`+Comp.farnesol,
G.FAR=`Comp.beta-farnesene`+`Comp.Z-E-alpha-farnesene`+`Comp.E-E-alpha-farnesene`+`Comp.farnesene-epoxide`,
G.SES=Comp.nerolidol+Comp.isophytol,
G.NER=Comp.nerolidol,
G.ISO=Comp.isophytol,
G.ALT=`Comp.alpha-terpineol`)
ER_f_mass_group_data <- ER_f_mass_groups %>% select(starts_with("G."))
ER_f_mass_group_data <- ER_f_mass_group_data %>% slice(.,-c(36,44))
ER_f_mass_groups <- ER_f_mass_groups %>% slice(.,-c(36,44))ILE group:
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: G.ILE ~ Population + (1 | Pop_Plant)
## Data: ER_f_mass_groups
##
## REML criterion at convergence: 2664.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.2608 -0.4180 -0.1058 0.2763 3.2117
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 2028620 1424
## Residual 1358393 1166
## Number of obs: 155, groups: Pop_Plant, 72
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 624.99 371.84 70.60 1.681 0.09722 .
## PopulationZion 1539.41 690.55 76.90 2.229 0.02872 *
## PopulationInyo 834.59 580.45 73.55 1.438 0.15472
## PopulationArizona 1463.53 488.52 67.01 2.996 0.00383 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnZ PpltnI
## PopulatinZn -0.538
## PopulatnIny -0.641 0.345
## PopultnArzn -0.761 0.410 0.488ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 13900701 4633567 3 72.587 3.4111 0.02191 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Logan 625 372 67.7 -118 1368
## Zion 2164 582 76.7 1005 3324
## Inyo 1460 446 72.8 570 2349
## Arizona 2089 317 59.6 1454 2723
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Logan - Zion -1539.4 691 74.0 -2.227 0.1254
## Logan - Inyo -834.6 581 70.6 -1.436 0.4814
## Logan - Arizona -1463.5 489 64.2 -2.992 0.0200
## Zion - Inyo 704.8 733 75.2 0.961 0.7719
## Zion - Arizona 75.9 663 72.4 0.114 0.9995
## Inyo - Arizona -628.9 547 68.0 -1.149 0.6607
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 4 estimates
Interpretation: Arizona has higher ILE emissions than Logan. All other contrasts are non-significant.
LEU group:
Diagnostics for the model residuals:
Untransformed residuals look okay, square root transformation (not shown) is comparable and doesn’t affect the results.
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: G.LEU ~ Population + (1 | Pop_Plant)
## Data: ER_f_mass_groups
##
## REML criterion at convergence: 2841.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8229 -0.3741 -0.0457 0.2252 4.2610
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 6125293 2475
## Residual 4507075 2123
## Number of obs: 155, groups: Pop_Plant, 72
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 322.25 654.99 63.57 0.492 0.624422
## PopulationZion 1933.11 1218.30 70.45 1.587 0.117052
## PopulationInyo 4576.09 1023.23 66.80 4.472 3.08e-05 ***
## PopulationArizona 3140.07 859.72 59.91 3.652 0.000548 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnZ PpltnI
## PopulatinZn -0.538
## PopulatnIny -0.640 0.344
## PopultnArzn -0.762 0.410 0.488ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 103931007 34643669 3 65.815 7.6865 0.0001768 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Logan 322 656 67.4 -987 1632
## Zion 2255 1028 77.4 209 4302
## Inyo 4898 787 73.1 3330 6467
## Arizona 3462 558 59.0 2346 4578
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Logan - Zion -1933 1219 74.4 -1.585 0.3932
## Logan - Inyo -4576 1025 70.7 -4.466 0.0002
## Logan - Arizona -3140 861 63.7 -3.647 0.0029
## Zion - Inyo -2643 1295 75.8 -2.042 0.1821
## Zion - Arizona -1207 1169 72.8 -1.032 0.7312
## Inyo - Arizona 1436 964 68.0 1.489 0.4497
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 4 estimates
Interpretation: Inyo and Arizona have higher emission rates of LEU compounds relative to Logan.
linalool:
Diagnostics for the model residuals:
Untransformed residuals look okay, square root transformation (not shown) is comparable and doesn’t affect the results.
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: G.LIN ~ Population + (1 | Pop_Plant)
## Data: ER_f_mass_groups
##
## REML criterion at convergence: 3004.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.9098 -0.3302 -0.0991 0.1478 3.5530
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 9909569 3148
## Residual 16565500 4070
## Number of obs: 155, groups: Pop_Plant, 72
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 2337.79 970.89 52.93 2.408 0.0196 *
## PopulationZion 3479.35 1840.99 67.84 1.890 0.0630 .
## PopulationInyo 7050.58 1531.40 60.04 4.604 2.20e-05 ***
## PopulationArizona 5678.78 1263.20 48.51 4.496 4.32e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnZ PpltnI
## PopulatinZn -0.527
## PopulatnIny -0.634 0.334
## PopultnArzn -0.769 0.405 0.487ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 464043699 154681233 3 58.846 9.3376 3.851e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Logan 2338 975 63.3 389 4287
## Zion 5817 1566 85.7 2703 8931
## Inyo 9388 1187 76.3 7024 11753
## Arizona 8017 811 52.4 6389 9644
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Logan - Zion -3479 1845 78.8 -1.886 0.2425
## Logan - Inyo -7051 1537 70.8 -4.589 0.0001
## Logan - Arizona -5679 1269 58.5 -4.477 0.0002
## Zion - Inyo -3571 1965 82.2 -1.817 0.2727
## Zion - Arizona -2199 1764 77.2 -1.247 0.5991
## Inyo - Arizona 1372 1438 67.6 0.954 0.7757
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 4 estimates
Interpretation: Inyo and Arizona emit more linalool than Logan.
alpha terpineol:
Diagnostics for the model residuals:
Square-root transformation applied to improve residuals.
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(G.ALT) ~ Population + (1 | Pop_Plant)
## Data: ER_f_mass_groups
##
## REML criterion at convergence: 570.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.68791 -0.47838 -0.04125 0.63549 2.29612
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 0.665 0.8155
## Residual 1.841 1.3570
## Number of obs: 155, groups: Pop_Plant, 72
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.58687 0.28542 66.07693 5.560 5.24e-07 ***
## PopulationZion -0.05045 0.55029 89.02134 -0.092 0.9272
## PopulationInyo -0.85800 0.45411 77.34429 -1.889 0.0626 .
## PopulationArizona 1.81384 0.36943 61.05085 4.910 7.14e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnZ PpltnI
## PopulatinZn -0.519
## PopulatnIny -0.629 0.326
## PopultnArzn -0.773 0.401 0.486ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 92.35 30.783 3 75.906 16.718 1.965e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population response SE df lower.CL upper.CL
## Logan 2.518 0.912 59.2 1.023476 4.67
## Zion 2.361 1.448 92.4 0.360621 6.11
## Inyo 0.531 0.517 78.6 0.000543 2.06
## Arizona 11.565 1.604 48.0 8.564666 15.01
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
## Intervals are back-transformed from the sqrt scale
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Logan - Zion 0.0505 0.552 82.0 0.091 0.9997
## Logan - Inyo 0.8580 0.456 70.2 1.880 0.2459
## Logan - Arizona -1.8138 0.372 54.3 -4.878 0.0001
## Zion - Inyo 0.8076 0.590 87.2 1.369 0.5218
## Zion - Arizona -1.8643 0.527 81.0 -3.538 0.0037
## Inyo - Arizona -2.6718 0.426 67.4 -6.276 <.0001
##
## Note: contrasts are still on the sqrt scale
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 4 estimates
Interpretation: Arizona has higher emission rates of alpha terpineol than all other populations.
FAR group–correlated with CAP2 only:
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: G.FAR ~ Population + (1 | Pop_Plant)
## Data: ER_f_mass_groups
##
## REML criterion at convergence: 2618.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.1113 -0.1234 -0.0005 -0.0001 5.0705
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 2282509 1510.8
## Residual 797229 892.9
## Number of obs: 155, groups: Pop_Plant, 72
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1352.69 366.14 69.69 3.694 0.000435 ***
## PopulationZion -1323.71 674.57 72.74 -1.962 0.053552 .
## PopulationInyo -470.98 569.43 71.06 -0.827 0.410944
## PopulationArizona -1351.25 483.72 67.32 -2.793 0.006785 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnZ PpltnI
## PopulatinZn -0.543
## PopulatnIny -0.643 0.349
## PopultnArzn -0.757 0.411 0.487ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 7355896 2451965 3 70.373 3.0756 0.03309 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Logan 1352.69 366 68.6 621.8 2084
## Zion 28.98 567 72.9 -1100.4 1158
## Inyo 881.71 436 70.9 11.8 1752
## Arizona 1.45 316 63.2 -630.5 633
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Logan - Zion 1323.7 675 71.6 1.962 0.2122
## Logan - Inyo 471.0 570 69.9 0.827 0.8416
## Logan - Arizona 1351.2 484 66.2 2.792 0.0337
## Zion - Inyo -852.7 715 72.2 -1.192 0.6336
## Zion - Arizona 27.5 649 70.5 0.042 1.0000
## Inyo - Arizona 880.3 539 68.1 1.634 0.3669
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 4 estimates
Interpretation: Logan emits more FAR compounds than Arizona.
OCI group–correlated with CAP2 only:
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: G.OCI ~ Population + (1 | Pop_Plant)
## Data: ER_f_mass_groups
##
## REML criterion at convergence: 2529.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.7155 -0.1261 -0.0546 0.0008 5.4062
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 1812563 1346.3
## Residual 354429 595.3
## Number of obs: 155, groups: Pop_Plant, 72
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 898.92 312.78 70.71 2.874 0.00535 **
## PopulationZion -873.13 573.97 72.31 -1.521 0.13257
## PopulationInyo -887.43 485.58 71.40 -1.828 0.07179 .
## PopulationArizona -55.93 414.68 69.20 -0.135 0.89310
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnZ PpltnI
## PopulatinZn -0.545
## PopulatnIny -0.644 0.351
## PopultnArzn -0.754 0.411 0.486ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 1998661 666220 3 70.946 1.8797 0.1408No differences across populations.
Floral morphology, multivariate analyses
In order to do multivariate analyses of the morphological variables, I had to drop leaf number and leaf length, because there isn’t enough data.
##
## Call:
## adonis(formula = morph_data ~ Population, data = morph_names, permutations = 999, method = "bray")
##
## Permutation: free
## Number of permutations: 999
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## Population 3 0.24907 0.083024 8.8739 0.38795 0.001 ***
## Residuals 42 0.39295 0.009356 0.61205
## Total 45 0.64203 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Interpretation: There is a significant effect of Population. It explains about 39 % of the variation in morphology.
Running a constrained analysis of principle coordinates:
##
## Call:
## capscale(formula = morph_data ~ Population, data = morph_names, distance = "bray")
##
## Partitioning of squared Bray distance:
## Inertia Proportion
## Total 0.7698 1.0000
## Constrained 0.2544 0.3305
## Unconstrained 0.5154 0.6695
##
## Eigenvalues, and their contribution to the squared Bray distance
##
## Importance of components:
## CAP1 CAP2 CAP3 MDS1 MDS2 MDS3 MDS4
## Eigenvalue 0.2042 0.04793 0.002334 0.2299 0.07166 0.04561 0.04071
## Proportion Explained 0.2652 0.06227 0.003032 0.2986 0.09308 0.05925 0.05289
## Cumulative Proportion 0.2652 0.32748 0.330511 0.6292 0.72224 0.78149 0.83438
## MDS5 MDS6 MDS7 MDS8 MDS9 MDS10 MDS11
## Eigenvalue 0.03430 0.02234 0.01351 0.01195 0.01082 0.007396 0.006189
## Proportion Explained 0.04456 0.02902 0.01755 0.01553 0.01406 0.009608 0.008040
## Cumulative Proportion 0.87894 0.90796 0.92551 0.94104 0.95510 0.964707 0.972747
## MDS12 MDS13 MDS14 MDS15 MDS16 MDS17
## Eigenvalue 0.005308 0.004060 0.003038 0.002506 0.001943 0.001320
## Proportion Explained 0.006895 0.005274 0.003946 0.003256 0.002525 0.001715
## Cumulative Proportion 0.979642 0.984917 0.988863 0.992119 0.994643 0.996358
## MDS18 MDS19 MDS20 MDS21 MDS22
## Eigenvalue 0.000988 0.0008716 0.0004951 0.0003749 7.392e-05
## Proportion Explained 0.001283 0.0011322 0.0006432 0.0004870 9.603e-05
## Cumulative Proportion 0.997642 0.9987738 0.9994170 0.9999040 1.000e+00
##
## Accumulated constrained eigenvalues
## Importance of components:
## CAP1 CAP2 CAP3
## Eigenvalue 0.2042 0.04793 0.002334
## Proportion Explained 0.8024 0.18840 0.009175
## Cumulative Proportion 0.8024 0.99083 1.000000
##
## Scaling 2 for species and site scores
## * Species are scaled proportional to eigenvalues
## * Sites are unscaled: weighted dispersion equal on all dimensions
## * General scaling constant of scores:The constrained portion explains about 33% of overall distance. CAP1 explains about 27% and CAP2 expalins about 6% of overall distance.
Plotting the capscale:
Checking to see which traits are significantly correlated with CAP1 and/or CAP2.
| variables | cor1 | p1 | cor2 | p2 | sig1 | sig2 |
|---|---|---|---|---|---|---|
| M.Corolla_D1 | 0.2619 | 0.0886 | 0.0846 | 0.6481 | No | No |
| M.Corolla_D2 | 0.7326 | 0.0000 | 0.3963 | 0.0144 | Yes | No |
| M.Tube_Flare | 0.5669 | 0.0001 | 0.2913 | 0.0636 | Yes | No |
| M.Stamen_Length | 0.669 | 0.0000 | 0.3271 | 0.0398 | Yes | No |
| M.Style_Length | 0.5906 | 0.0000 | 0.4047 | 0.0144 | Yes | No |
| M.Hypanthium_Length | 0.6229 | 0.0000 | -0.5591 | 0.0002 | Yes | Yes |
| M.Pedicel_Length | -0.2391 | 0.1096 | 0.5711 | 0.0002 | No | Yes |
| M.Nectar_Column | 0.79 | 0.0000 | -0.3636 | 0.0234 | Yes | No |
| M.Percent_Sugar | 0.5667 | 0.0001 | -0.0442 | 0.7704 | Yes | No |
From this, all variables except for pedicel length and Corolla D1 are correlated with CAP1, and all of them are positively correlated.
The only variables correlated with CAP2 are hypanthium length (negative) and pedicel length (positive).
Floral morphology, univariate analyses
Looking at all nine floral morphology variables, as all were correlated with CAP1 and/or CAP2. Each variable is modeled as a function of population, with plant nested within population as a random effect. This uses data from all measured flowers where all variables were measured on the flower.
Corolla D2:
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: M.Corolla_D2 ~ Population + (1 | Pop_Plant)
## Data: morph_names
##
## REML criterion at convergence: 740.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.6251 -0.4669 -0.0388 0.4354 1.8214
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 36.01 6.001
## Residual 23.67 4.865
## Number of obs: 113, groups: Pop_Plant, 63
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 76.002 1.736 54.173 43.780 < 2e-16 ***
## PopulationZion 24.461 3.168 62.518 7.720 1.15e-10 ***
## PopulationInyo 14.396 2.678 58.110 5.375 1.42e-06 ***
## PopulationArizona 8.029 2.239 53.095 3.585 0.000732 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnZ PpltnI
## PopulatinZn -0.548
## PopulatnIny -0.648 0.355
## PopultnArzn -0.775 0.425 0.502ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 1618.3 539.44 3 58.663 22.791 6.616e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Logan 76.0 1.74 56.3 72.5 79.5
## Zion 100.5 2.65 68.5 95.2 105.8
## Inyo 90.4 2.04 63.2 86.3 94.5
## Arizona 84.0 1.42 53.6 81.2 86.9
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Logan - Zion -24.46 3.17 64.6 -7.713 <.0001
## Logan - Inyo -14.40 2.68 60.2 -5.369 <.0001
## Logan - Arizona -8.03 2.24 55.2 -3.580 0.0039
## Zion - Inyo 10.07 3.35 66.5 3.007 0.0190
## Zion - Arizona 16.43 3.01 64.9 5.464 <.0001
## Inyo - Arizona 6.37 2.48 60.0 2.562 0.0607
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 4 estimates
Interpretation: Zion has a significantly larger corolla dimension 2 relative to all other populations. Inyo and Arizona have the next largest corolla D2, which is larger than Logan.
Tube Flare:
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: M.Tube_Flare ~ Population + (1 | Pop_Plant)
## Data: morph_names
##
## REML criterion at convergence: 329
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.9872 -0.5545 -0.0399 0.5449 3.6777
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 0.5596 0.748
## Residual 0.6676 0.817
## Number of obs: 113, groups: Pop_Plant, 63
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 8.0467 0.2395 54.3746 33.591 < 2e-16 ***
## PopulationZion 1.9806 0.4446 67.3043 4.455 3.25e-05 ***
## PopulationInyo 1.0110 0.3726 60.4772 2.713 0.00866 **
## PopulationArizona 0.4937 0.3083 52.8497 1.601 0.11530
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnZ PpltnI
## PopulatinZn -0.539
## PopulatnIny -0.643 0.346
## PopultnArzn -0.777 0.419 0.499ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 14.816 4.9388 3 61.085 7.3982 0.0002629 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Logan 8.05 0.240 54.2 7.56 8.53
## Zion 10.03 0.375 73.1 9.28 10.77
## Inyo 9.06 0.286 65.0 8.49 9.63
## Arizona 8.54 0.195 50.5 8.15 8.93
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Logan - Zion -1.981 0.445 67.2 -4.447 0.0002
## Logan - Inyo -1.011 0.374 60.3 -2.707 0.0427
## Logan - Arizona -0.494 0.309 52.7 -1.596 0.3896
## Zion - Inyo 0.970 0.472 70.0 2.056 0.1779
## Zion - Arizona 1.487 0.423 67.7 3.519 0.0042
## Inyo - Arizona 0.517 0.346 60.0 1.495 0.4467
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 4 estimates
Interpretation: Zion is equal to Inyo, but greater than Arizona or Logan. Inyo is equal to Arizona, and greater than Logan. Arizona and Logan are equivalent.
Stamen Length:
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: M.Stamen_Length ~ Population + (1 | Pop_Plant)
## Data: morph_names
##
## REML criterion at convergence: 606.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.37343 -0.44195 0.01174 0.48588 2.92579
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 7.989 2.826
## Residual 8.051 2.837
## Number of obs: 113, groups: Pop_Plant, 63
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 23.8270 0.8763 55.4607 27.191 < 2e-16 ***
## PopulationZion 14.3475 1.6180 66.9277 8.868 6.67e-13 ***
## PopulationInyo 7.5720 1.3596 60.8809 5.569 6.13e-07 ***
## PopulationArizona 2.8949 1.1286 54.0655 2.565 0.0131 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnZ PpltnI
## PopulatinZn -0.542
## PopulatnIny -0.645 0.349
## PopultnArzn -0.776 0.421 0.500ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 744.35 248.12 3 61.491 30.819 2.762e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Logan 23.8 0.879 54.9 22.1 25.6
## Zion 38.2 1.362 71.7 35.5 40.9
## Inyo 31.4 1.041 64.5 29.3 33.5
## Arizona 26.7 0.713 51.5 25.3 28.2
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Logan - Zion -14.35 1.62 66.4 -8.854 <.0001
## Logan - Inyo -7.57 1.36 60.3 -5.558 <.0001
## Logan - Arizona -2.89 1.13 53.5 -2.558 0.0624
## Zion - Inyo 6.78 1.71 69.0 3.953 0.0010
## Zion - Arizona 11.45 1.54 66.9 7.451 <.0001
## Inyo - Arizona 4.68 1.26 60.0 3.706 0.0025
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 4 estimates
Interpretation: Zion has longer stamens then all other populations. Inyo has longer stamens than Logan and Arizona. Logan and Arizona have comparable stamens.
Style Length:
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: M.Style_Length ~ Population + (1 | Pop_Plant)
## Data: morph_names
##
## REML criterion at convergence: 666.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.11023 -0.44380 -0.02053 0.39063 2.91571
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 13.83 3.719
## Residual 14.11 3.757
## Number of obs: 113, groups: Pop_Plant, 63
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 25.629 1.156 50.125 22.178 < 2e-16 ***
## PopulationZion 13.594 2.135 61.865 6.369 2.65e-08 ***
## PopulationInyo 7.516 1.793 55.613 4.191 0.0001 ***
## PopulationArizona 1.211 1.488 48.733 0.814 0.4197
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnZ PpltnI
## PopulatinZn -0.541
## PopulatnIny -0.644 0.349
## PopultnArzn -0.776 0.420 0.500ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 780.9 260.3 3 56.228 18.446 1.869e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Logan 25.6 1.16 54.8 23.3 28.0
## Zion 39.2 1.80 71.8 35.6 42.8
## Inyo 33.1 1.37 64.5 30.4 35.9
## Arizona 26.8 0.94 51.4 25.0 28.7
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Logan - Zion -13.59 2.14 66.4 -6.359 <.0001
## Logan - Inyo -7.52 1.80 60.3 -4.182 0.0005
## Logan - Arizona -1.21 1.49 53.4 -0.812 0.8486
## Zion - Inyo 6.08 2.26 69.0 2.687 0.0437
## Zion - Arizona 12.38 2.03 66.9 6.106 <.0001
## Inyo - Arizona 6.30 1.66 60.0 3.787 0.0020
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 4 estimates
Interpretation: Zion has longer styles then all other populations. Inyo has longer styles than Logan and Arizona. Logan and Arizona have comparable styles.
Hypanthium Length:
Diagnostics for the model residuals:
It looks like there is one outlier: rm2-28 (Arizona) the fifth flower, measured on 6/19. It has a length of 36.48, but the other four flowers from the plant all have lengths over 100. I suspect that the 100 digit may have been dropped from this measurement. Can we either resolve this from the paper datasheet or remove this outlier?
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: M.Hypanthium_Length ~ Population + (1 | Pop_Plant)
## Data: morph_names
##
## REML criterion at convergence: 940.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.9581 -0.4133 0.0357 0.3920 1.9928
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 30.71 5.541
## Residual 264.19 16.254
## Number of obs: 113, groups: Pop_Plant, 63
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 91.844 3.238 50.519 28.360 < 2e-16 ***
## PopulationZion 29.713 6.414 80.211 4.633 1.38e-05 ***
## PopulationInyo 37.806 5.208 65.042 7.259 6.01e-10 ***
## PopulationArizona 43.706 4.135 47.631 10.571 4.38e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnZ PpltnI
## PopulatinZn -0.505
## PopulatnIny -0.622 0.314
## PopultnArzn -0.783 0.396 0.487ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 31070 10357 3 63.838 39.202 1.732e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Logan 91.8 3.28 44.9 85.2 98.4
## Zion 121.6 5.55 88.3 110.5 132.6
## Inyo 129.6 4.10 70.8 121.5 137.8
## Arizona 135.5 2.61 38.1 130.3 140.8
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Logan - Zion -29.71 6.45 75.6 -4.607 0.0001
## Logan - Inyo -37.81 5.25 59.5 -7.199 <.0001
## Logan - Arizona -43.71 4.19 42.1 -10.437 <.0001
## Zion - Inyo -8.09 6.91 82.1 -1.172 0.6461
## Zion - Arizona -13.99 6.14 77.3 -2.281 0.1114
## Inyo - Arizona -5.90 4.86 59.4 -1.214 0.6206
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 4 estimates
Interpretation: Logan is lower than the other three populations, which are comparable.
Pedicel length:
Note: there are some potential outliers/zeros values that maybe should be NAs in the dataset right now.
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: M.Pedicel_Length ~ Population + (1 | Pop_Plant)
## Data: morph_names
##
## REML criterion at convergence: 721
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.3082 -0.4655 -0.1300 0.5969 2.5099
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 24.75 4.975
## Residual 22.20 4.712
## Number of obs: 113, groups: Pop_Plant, 63
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 16.554 1.511 47.372 10.957 1.39e-14 ***
## PopulationZion 2.093 2.780 58.051 0.753 0.454554
## PopulationInyo -3.700 2.340 52.341 -1.581 0.119927
## PopulationArizona -6.953 1.947 46.092 -3.572 0.000844 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnZ PpltnI
## PopulatinZn -0.543
## PopulatnIny -0.646 0.351
## PopultnArzn -0.776 0.422 0.501ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 421.92 140.64 3 52.944 6.3352 0.0009442 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Logan 16.6 1.51 55.3 13.52 19.6
## Zion 18.6 2.34 70.8 13.99 23.3
## Inyo 12.9 1.79 64.1 9.28 16.4
## Arizona 9.6 1.23 52.1 7.13 12.1
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Logan - Zion -2.09 2.78 65.9 -0.752 0.8755
## Logan - Inyo 3.70 2.34 60.3 1.578 0.3987
## Logan - Arizona 6.95 1.95 54.0 3.564 0.0042
## Zion - Inyo 5.79 2.94 68.2 1.968 0.2101
## Zion - Arizona 9.05 2.64 66.3 3.426 0.0057
## Inyo - Arizona 3.25 2.17 60.0 1.498 0.4452
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 4 estimates
Interpretation: The only significant contrasts are that Logan and Zion have larger pedicel lengths than Arizona.
Nectar column:
Note: there are some potential outliers/zeros values that maybe should be NAs in the dataset right now.
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: M.Nectar_Column ~ Population + (1 | Pop_Plant)
## Data: morph_names
##
## REML criterion at convergence: 1187.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.7651 -0.5456 -0.0139 0.3381 5.4212
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 249 15.78
## Residual 2584 50.84
## Number of obs: 113, groups: Pop_Plant, 63
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 30.774 9.949 37.385 3.093 0.00374 **
## PopulationZion 49.809 19.794 69.610 2.516 0.01416 *
## PopulationInyo 43.471 16.038 52.061 2.710 0.00908 **
## PopulationArizona 74.193 12.694 34.702 5.845 1.28e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnZ PpltnI
## PopulatinZn -0.503
## PopulatnIny -0.620 0.312
## PopultnArzn -0.784 0.394 0.486ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 88513 29504 3 50.452 11.416 7.922e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Estimated marginal means & contrasts across populations:
## $emmeans
## Population emmean SE df lower.CL upper.CL
## Logan 30.8 10.1 44.3 10.5 51.1
## Zion 80.6 17.2 89.2 46.5 114.7
## Inyo 74.2 12.7 71.2 49.0 99.5
## Arizona 105.0 8.0 37.2 88.8 121.2
##
## Degrees-of-freedom method: kenward-roger
## Confidence level used: 0.95
##
## $contrasts
## contrast estimate SE df t.ratio p.value
## Logan - Zion -49.81 19.9 76.1 -2.502 0.0676
## Logan - Inyo -43.47 16.2 59.4 -2.687 0.0449
## Logan - Arizona -74.19 12.9 41.4 -5.766 <.0001
## Zion - Inyo 6.34 21.3 82.9 0.297 0.9908
## Zion - Arizona -24.38 18.9 78.0 -1.287 0.5737
## Inyo - Arizona -30.72 15.0 59.4 -2.051 0.1812
##
## Degrees-of-freedom method: kenward-roger
## P value adjustment: tukey method for comparing a family of 4 estimates
Interpretation: Logan is lower than Arizona and Inyo.
Percent sugar:
Note: there are some potential outliers/zeros values that maybe should be NAs in the dataset right now.
Diagnostics for the model residuals:
Model summary:
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: M.Percent_Sugar ~ Population + (1 | Pop_Plant)
## Data: morph_names
##
## REML criterion at convergence: 700.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.1849 -0.2773 0.1092 0.4407 1.8411
##
## Random effects:
## Groups Name Variance Std.Dev.
## Pop_Plant (Intercept) 9.04 3.007
## Residual 24.78 4.978
## Number of obs: 113, groups: Pop_Plant, 63
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 23.2058 1.1812 43.0687 19.645 <2e-16 ***
## PopulationZion 4.7336 2.2560 64.2276 2.098 0.0398 *
## PopulationInyo 4.0450 1.8640 52.7764 2.170 0.0345 *
## PopulationArizona 0.9482 1.5148 41.0303 0.626 0.5348
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) PpltnZ PpltnI
## PopulatinZn -0.524
## PopulatnIny -0.634 0.332
## PopultnArzn -0.780 0.408 0.494ANOVA:
## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## Population 194.09 64.698 3 52.978 2.6105 0.06095 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Anova is not significant.
Multivariate analysis of scent and morphology together
##
## Call:
## adonis(formula = All_data ~ Population, data = All_data_names, permutations = 999, method = "bray")
##
## Permutation: free
## Number of permutations: 999
##
## Terms added sequentially (first to last)
##
## Df SumsOfSqs MeanSqs F.Model R2 Pr(>F)
## Population 3 2.1856 0.72855 4.967 0.26656 0.001 ***
## Residuals 41 6.0138 0.14668 0.73344
## Total 44 8.1994 1.00000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Population explains about 28 % of the variation in percent composition of floral scent and in morphology. (As a reminder, population explained about 23 % of variation in the scent only dataset, and about 39 % of variation in the morphology only dataset.)
Running a constrained analysis of principle coordinates:
##
## Call:
## capscale(formula = All_data ~ Population, data = All_data_names, distance = "bray")
##
## Partitioning of squared Bray distance:
## Inertia Proportion
## Total 9.071 1.0000
## Constrained 2.244 0.2474
## Unconstrained 6.827 0.7526
##
## Eigenvalues, and their contribution to the squared Bray distance
##
## Importance of components:
## CAP1 CAP2 CAP3 MDS1 MDS2 MDS3 MDS4
## Eigenvalue 1.9963 0.13405 0.11345 2.0705 1.2325 0.84055 0.7430
## Proportion Explained 0.2201 0.01478 0.01251 0.2282 0.1359 0.09266 0.0819
## Cumulative Proportion 0.2201 0.23485 0.24736 0.4756 0.6115 0.70414 0.7860
## MDS5 MDS6 MDS7 MDS8 MDS9 MDS10 MDS11
## Eigenvalue 0.54344 0.38177 0.24733 0.15272 0.11559 0.10850 0.09278
## Proportion Explained 0.05991 0.04209 0.02727 0.01684 0.01274 0.01196 0.01023
## Cumulative Proportion 0.84595 0.88804 0.91530 0.93214 0.94488 0.95684 0.96707
## MDS12 MDS13 MDS14 MDS15 MDS16 MDS17
## Eigenvalue 0.074755 0.050659 0.044638 0.039513 0.02576 0.02350
## Proportion Explained 0.008241 0.005585 0.004921 0.004356 0.00284 0.00259
## Cumulative Proportion 0.975312 0.980896 0.985817 0.990173 0.99301 0.99560
## MDS18 MDS19 MDS20 MDS21 MDS22 MDS23
## Eigenvalue 0.014872 0.009476 0.0080610 0.0044234 0.0023432 7.074e-04
## Proportion Explained 0.001639 0.001045 0.0008886 0.0004876 0.0002583 7.798e-05
## Cumulative Proportion 0.997243 0.998287 0.9991761 0.9996637 0.9999220 1.000e+00
##
## Accumulated constrained eigenvalues
## Importance of components:
## CAP1 CAP2 CAP3
## Eigenvalue 1.9963 0.13405 0.11345
## Proportion Explained 0.8897 0.05974 0.05056
## Cumulative Proportion 0.8897 0.94944 1.00000
##
## Scaling 2 for species and site scores
## * Species are scaled proportional to eigenvalues
## * Sites are unscaled: weighted dispersion equal on all dimensions
## * General scaling constant of scores:The constrained portion explains about 26% of overall distance. CAP1 explains about 24% and CAP2 expalins about 1.5% of overall distance.
Plotting the capscale:
Checking to see which compound group(s) are significantly correlated with CAP1 and/or CAP2.
| variables | cor1 | p1 | cor2 | p2 | sig1 | sig2 |
|---|---|---|---|---|---|---|
| M.Corolla_D1 | 0.38 | 0.0422 | -0.1507 | 0.4844 | No | No |
| M.Corolla_D2 | 0.2573 | 0.1678 | -0.1815 | 0.4844 | No | No |
| M.Tube_Flare | 0.1703 | 0.3871 | -0.132 | 0.5086 | No | No |
| M.Stamen_Length | 0.306 | 0.1228 | -0.1561 | 0.4844 | No | No |
| M.Style_Length | 0.2915 | 0.1324 | -0.2437 | 0.3737 | No | No |
| M.Hypanthium_Length | 0.6106 | 0.0001 | 0.0407 | 0.8973 | Yes | No |
| M.Pedicel_Length | -0.2168 | 0.2463 | -0.0325 | 0.8973 | No | No |
| M.Nectar_Column | 0.2682 | 0.1572 | 0.0281 | 0.8973 | No | No |
| M.Percent_Sugar | 0.1181 | 0.5433 | -0.2299 | 0.3859 | No | No |
| G.ILE | 0.458 | 0.0082 | -0.3256 | 0.2035 | Yes | No |
| G.LEU | 0.5587 | 0.0005 | -0.4794 | 0.0091 | Yes | Yes |
| G.PHE | -0.0748 | 0.7295 | 0.1578 | 0.4844 | No | No |
| G.OCI | -0.0652 | 0.7369 | 0.1696 | 0.4844 | No | No |
| G.GER | 0.1658 | 0.3871 | -0.2725 | 0.2947 | No | No |
| G.LIN | 0.7372 | 0.0000 | -0.508 | 0.0077 | Yes | Yes |
| G.LOX | 0.0076 | 0.9606 | 0.0123 | 0.9359 | No | No |
| G.CAR | -0.309 | 0.1228 | -0.1856 | 0.4844 | No | No |
| G.FAR | -0.0587 | 0.7369 | -0.1405 | 0.5004 | No | No |
| G.SES | 0.2861 | 0.1324 | -0.1846 | 0.4844 | No | No |
| G.NER | 0.1491 | 0.4311 | -0.2786 | 0.2947 | No | No |
| G.ISO | 0.2432 | 0.1879 | -0.0981 | 0.6444 | No | No |
| G.ALT | 0.38 | 0.0422 | -0.1507 | 0.4844 | No | No |
Correlated with CAP 1: Corolla D2 (+), Tube flare (+), Stamen length (+), Style length (+), Hypanthium Length (+), Nectar Column (+), Percent sugar (+), LEU (+), PHE (+), OCI (+), GER (+), LIN (+), CAR (+), FAR (+), NER (+), ISO (+), ALT (+)
Correlated with CAP 2: Hypanthium Length (-), Pedicel Length (+), LIN (-), LOX (+)